chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...

, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of

oxidation Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or ...

(loss of

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

s) of an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...

in a

chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...

. Conceptually, the oxidation state may be positive, negative or zero. While fully ionic bonds are not found in nature, many bonds exhibit strong ionicity, making oxidation state a useful predictor of charge. The oxidation state of an atom does not represent the "real"

formal charge In chemistry, a formal charge (F.C. or q), in the covalent view of chemical bonding, is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electro ...

on that atom, or any other actual atomic property. This is particularly true of high oxidation states, where the

ionization energy Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule ...

required to produce a multiply positive ion is far greater than the energies available in chemical reactions. Additionally, the oxidation states of atoms in a given compound may vary depending on the choice of

electronegativity Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the ...

scale used in their calculation. Thus, the oxidation state of an atom in a compound is purely a formalism. It is nevertheless important in understanding the nomenclature conventions of inorganic compounds. Also, several observations regarding chemical reactions may be explained at a basic level in terms of oxidation states. Oxidation states are typically represented by

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...

s which may be positive, zero, or negative. In some cases, the average oxidation state of an element is a fraction, such as for

iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...

magnetite Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...

( see below). The highest known oxidation state is reported to be +9, displayed by

iridium Iridium is a chemical element with the symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) with a density o ...

in the tetroxoiridium(IX) cation (). It is predicted that even a +10 oxidation state may be achieved by

platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...

in tetroxoplatinum(X), . The lowest oxidation state is −5, as for

boron Boron is a chemical element with the symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the '' boron group'' it has t ...

in . In inorganic nomenclature, the oxidation state is represented by a

Roman numeral Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, ea ...

placed after the element name inside the parenthesis or as a superscript after the element symbol, e.g.

Iron(III) oxide Iron(III) oxide or ferric oxide is the inorganic compound with the formula Fe2O3. It is one of the three main oxides of iron, the other two being iron(II) oxide (FeO), which is rare; and iron(II,III) oxide (Fe3O4), which also occurs naturally a ...

. The term ''oxidation'' was first used by

Antoine Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...

. Much later, it was realized that the substance, upon being oxidized, loses electrons, and the meaning was extended to include other

reactions Reaction may refer to a process or to a response to an action, event, or exposure: Physics and chemistry *Chemical reaction *Nuclear reaction * Reaction (physics), as defined by Newton's third law *Chain reaction (disambiguation). Biology and m ...

in which electrons are lost, regardless of whether oxygen was involved. The increase in the oxidation state of an atom, through a chemical reaction, is known as oxidation; a decrease in oxidation state is known as a reduction. Such reactions involve the formal transfer of electrons: a net gain in electrons being a reduction, and a net loss of electrons being oxidation. For pure elements, the oxidation state is zero.

IUPAC definition

IUPAC has published a "Comprehensive definition of the term oxidation state (IUPAC Recommendations 2016)". It is a distillation of an

IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...

technical report "Toward a comprehensive definition of oxidation state" from 2014. The current IUPAC ''

Gold Book The International Union of Pure and Applied Chemistry publishes many books which contain its complete list of definitions. The definitions are divided into seven "colour books": Gold, Green, Blue, Purple, Orange, White, and Red. There is also an e ...

'' definition of oxidation state is: and the term ''oxidation number'' is nearly synonymous. The underlying principle is that the ionic charge is "the oxidation state of an atom, after ionic approximation of its bonds", where ionic approximation means, hypothesizing that all bonds are ionic. Several criteria were considered for the ionic approximation: # Extrapolation of the bond’s polarity; # Assignment of electrons according to the atom’s contribution to the bonding

Molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of find ...

(MO)/ the electron's allegiance in a LCAO–MO model. In a bond between two different elements, the bond's electrons are assigned to its main atomic contributor/higher electronegativity; in a bond between two atoms of the same element, the electrons are divided equally. This is because most electronegativity scales depend on the atom's bonding state, which makes the assignment of the oxidation state a somewhat circular argument. For example, some scales may turn out unusual oxidation states, such as -6 for

in , for Pauling and Mulliken scales. The dipole moments would, sometimes, also turn out abnormal oxidation numbers, such as in CO and NO, which are oriented with their positive end towards oxygen. Therefore, this leaves the atom's contribution to the bonding MO, the atomic-orbital energy, and from quantum-chemical calculations of charges, as the only viable criteria with cogent values for ionic approximation. However, for a simple estimate for the ionic approximation, we can use Allen electronegativities, as only that electronegativity scale is truly independent of the oxidation state, as it relates to the average valence‐electron energy of the free atom:

Determination

While introductory levels of chemistry teaching use postulated oxidation states, the IUPAC recommendation and the ''Gold Book'' entry list two entirely general algorithms for the calculation of the oxidation states of elements in chemical compounds.

Simple approach without bonding considerations

Introductory chemistry uses postulates: the oxidation state for an element in a chemical formula is calculated from the overall charge and postulated oxidation states for all the other atoms. A simple example is based on two postulates, # OS = +1 for

hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...

# OS = −2 for

where OS stands for oxidation state. This approach yields correct oxidation states in oxides and hydroxides of any single element, and in acids such as H₂SO₄ or H₂Cr₂O₇. Its coverage can be extended either by a list of exceptions or by assigning priority to the postulates. The latter works for H₂O₂ where the priority of rule 1 leaves both oxygens with oxidation state −1. Additional postulates and their ranking may expand the range of compounds to fit a textbook's scope. As an example, one postulatory algorithm from many possible; in a sequence of decreasing priority: # An element in a free form has OS = 0. # In a compound or ion, the sum of the oxidation states equals the total charge of the compound or ion. #

Fluorine Fluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reactiv ...

in compounds has OS = −1; this extends to

chlorine Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...

and

bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table ( halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simi ...

only when not bonded to a lighter halogen, oxygen or nitrogen. #

Group 1 Group 1 may refer to: * Alkali metal, a chemical element classification for Alkali metal * Group 1 (racing), a historic (until 1981) classification for Touring car racing, applied to standard touring cars. Comparable to modern FIA Group N * Group On ...

and

group 2 The term Group 2 may refer to: * Alkaline earth metal, a chemical element classification * Astronaut Group 2, also known as The New Nine, the second group of astronauts selected by NASA in 1962 * Group 2 (racing) The Group 2 racing class referred ...

metals in compounds have OS = +1 and +2, respectively. # Hydrogen has OS = +1 but adopts −1 when bonded as a

hydride In chemistry, a hydride is formally the anion of hydrogen( H−). The term is applied loosely. At one extreme, all compounds containing covalently bound H atoms are called hydrides: water (H2O) is a hydride of oxygen, ammonia is a hydride ...

to metals or metalloids. # Oxygen in compounds has OS = −2 but only when not bonded to oxygen (e.g. in peroxides) or fluorine. This set of postulates covers oxidation states of fluorides, chlorides, bromides, oxides, hydroxides, and hydrides of any single element. It covers all oxoacids of any central atom (and all their fluoro-, chloro-, and bromo-relatives), as well as

salts In chemistry, a salt is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a compound with no net electric charge. A common example is table salt, with positively c ...

of such acids with group 1 and 2 metals. It also covers

iodide An iodide ion is the ion I−. Compounds with iodine in formal oxidation state −1 are called iodides. In everyday life, iodide is most commonly encountered as a component of iodized salt, which many governments mandate. Worldwide, iodine de ...

sulfide Sulfide (British English also sulphide) is an inorganic anion of sulfur with the chemical formula S2− or a compound containing one or more S2− ions. Solutions of sulfide salts are corrosive. ''Sulfide'' also refers to chemical compounds la ...

s, and similar simple salts of these metals.

Algorithm of assigning bonds

This algorithm is performed on a

Lewis structure Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons ...

(a diagram that shows all

valence electron In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair form ...

s). Oxidation state equals the charge of an atom after each of its

heteronuclear A heteronuclear molecule is a molecule composed of atoms of more than one chemical element. For example, a molecule of water (H2O) is heteronuclear because it has atoms of two different elements, hydrogen (H) and oxygen (O). Similarly, a heteronu ...

bonds has been assigned to the more-

electronegative Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the ...

partner of the bond ( except when that partner is a reversibly bonded Lewis-acid ligand) and

homonuclear Homonuclear molecules, or homonuclear species, are molecules composed of only one element. Homonuclear molecules may consist of various numbers of atoms. The size of the molecule an element can form depends on the element's properties, and some el ...

bonds have been divided equally: : 1oxstate

where each "—" represents an electron pair (either shared between two atoms or solely on one atom), and "OS" is the oxidation state as a numerical variable. After the electrons have been assigned according to the vertical red lines on the formula, the total number of valence electrons that now "belong" to each atom is subtracted from the number ''N'' of valence electrons of the neutral atom (such as 5 for nitrogen in group 15) to yield that atom's oxidation state. This example shows the importance of describing the bonding. Its summary formula, HNO₃, corresponds to two

structural isomer In chemistry, a structural isomer (or constitutional isomer in the IUPAC nomenclature) of a compound is another compound whose molecule has the same number of atoms of each element, but with logically distinct bonds between them. The term meta ...

s; the

peroxynitrous acid Peroxynitrous acid (HNO3) is a reactive nitrogen species (RNS). It is the conjugate acid of peroxynitrite (ONOO−). It has a p''K''a of approximately 6.8. It is formed ''in vivo'' from the diffusion-controlled reaction of nitrogen monoxide (ON ...

in the above figure and the more stable

nitric acid Nitric acid is the inorganic compound with the formula . It is a highly corrosive mineral acid. The compound is colorless, but older samples tend to be yellow cast due to decomposition into oxides of nitrogen. Most commercially available ni ...

. With the formula HNO₃, the simple approach without bonding considerations yields −2 for all three oxygens and +5 for nitrogen, which is correct for nitric acid. For the peroxynitrous acid, however, the two oxygens in the O–O bond each has OS = −1 and the nitrogen has OS = +3, which requires a structure to understand.

Organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. Th ...

s are treated in a similar manner; exemplified here on

functional group In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the r ...

s occurring in between CH₄ and CO₂: : 3oxstate

Analogously for

transition-metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...

compounds; on the left has a total of 36 valence electrons (18 pairs to be distributed), and on the right has 66 valence electrons (33 pairs): : 2oxstate

A key step is drawing the Lewis structure of the molecule (neutral, cationic, anionic): atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule (a sort of "skeletal" structure), and the remaining valence electrons are distributed such that sp atoms obtain an

octet Octet may refer to: Music * Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble ** String octet, a piece of music written for eight string instruments *** Octet (Mendelssohn), 1825 com ...

(duet for hydrogen) with a priority that increases in proportion with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders (the full set of which is called the resonance formulas). Consider the

sulfate The sulfate or sulphate ion is a polyatomic anion with the empirical formula . Salts, acid derivatives, and peroxides of sulfate are widely used in industry. Sulfates occur widely in everyday life. Sulfates are salts of sulfuric acid and many ...

anion ( with 32 valence electrons; 24 from oxygens, 6 from sulfur, 2 of the anion charge obtained from the implied cation). The

bond order In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds. The bond order itself is the number of electron pairs ( covalent bonds) between two atoms. For example, in diat ...

s to the terminal oxygens do not affect the oxidation state so long as the oxygens have octets. Already the skeletal structure, top left, yields the correct oxidation states, as does the Lewis structure, top right (one of the resonance formulas): : 7oxstate

The bond-order formula at the bottom is closest to the reality of four equivalent oxygens each having a total bond order of 2. That total includes the bond of order to the implied cation and follows the 8 − ''N'' rule requiring that the main-group atom's bond order equals 8 minus ''N'' valence electrons of the neutral atom, enforced with a priority that proportionately increases with electronegativity. This algorithm works equally for molecular cations composed of several atoms. An example is the

ammonium The ammonium cation is a positively-charged polyatomic ion with the chemical formula or . It is formed by the protonation of ammonia (). Ammonium is also a general name for positively charged or protonated substituted amines and quaterna ...

cation of 8 valence electrons (5 from nitrogen, 4 from hydrogens, minus 1 electron for the cation's positive charge): : 5oxstate

Drawing Lewis structures with electron pairs as dashes emphasizes the essential equivalence of bond pairs and lone pairs when counting electrons and moving bonds onto atoms. Structures drawn with electron dot pairs are of course identical in every way: : 4oxstate

The algorithm's caveat

The algorithm contains a caveat, which concerns rare cases of

complexes with a type of

ligand In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's elect ...

that is reversibly bonded as a

Lewis acid A Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any sp ...

(as an acceptor of the electron pair from the transition metal); termed a "Z-type" ligand in Green's covalent bond classification method. The caveat originates from the simplifying use of electronegativity instead of the MO-based electron allegiance to decide the ionic sign. One early example is the O₂S−RhCl(CO)( PPh₃)₂ complex with SO₂ as the reversibly-bonded acceptor ligand (released upon heating). The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of

rhodium Rhodium is a chemical element with the symbol Rh and atomic number 45. It is a very rare, silvery-white, hard, corrosion-resistant transition metal. It is a noble metal and a member of the platinum group. It has only one naturally occurring i ...

and sulfur, yielding oxidation state +1 for rhodium: : 8oxstate

Algorithm of summing bond orders

This algorithm works on Lewis structures and bond graphs of extended (non-molecular) solids:

Applied to a Lewis structure

An example of a Lewis structure with no formal charge, : 9oxstate

illustrates that, in this algorithm, homonuclear bonds are simply ignored (the bond orders are in blue). Carbon monoxide exemplifies a Lewis structure with formal charges: : 10oxstate

To obtain the oxidation states, the formal charges are summed with the bond-order value taken positively at the carbon and negatively at the oxygen. Applied to molecular ions, this algorithm considers the actual location of the formal (ionic) charge, as drawn in the Lewis structure. As an example, summing bond orders in the

cation yields −4 at the nitrogen of formal charge +1, with the two numbers adding to the oxidation state of −3: : 11oxstate

The sum of oxidation states in the ion equals its charge (as it equals zero for a neutral molecule). Also in anions, the formal (ionic) charges have to be considered when nonzero. For sulfate this is exemplified with the skeletal or Lewis structures (top), compared with the bond-order formula of all oxygens equivalent and fulfilling the octet and 8 − ''N'' rules (bottom): : 13oxstate

Applied to bond graph

A bond graph in solid-state chemistry is a chemical formula of an extended structure, in which direct bonding connectivities are shown. An example is the AuORb₃

perovskite Perovskite (pronunciation: ) is a calcium titanium oxide mineral composed of calcium titanate (chemical formula ). Its name is also applied to the class of compounds which have the same type of crystal structure as (XIIA2+VIB4+X2−3), known a ...

, the unit cell of which is drawn on the left and the bond graph (with added numerical values) on the right: : 14oxstate

We see that the oxygen atom bonds to the six nearest

rubidium Rubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher ...

cations, each of which has 4 bonds to the

auride Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile meta ...

anion. The bond graph summarizes these connectivities. The bond orders (also called

bond valence The bond valence method or mean method (or bond valence sum) (not to be mistaken for the valence bond theory in quantum chemistry) is a popular method in coordination chemistry to estimate the oxidation states of atoms. It is derived from the bond ...

s) sum up to oxidation states according to the attached sign of the bond's ionic approximation (there are no formal charges in bond graphs). Determination of oxidation states from a bond graph can be illustrated on

ilmenite Ilmenite is a titanium-iron oxide mineral with the idealized formula . It is a weakly magnetic black or steel-gray solid. Ilmenite is the most important ore of titanium and the main source of titanium dioxide, which is used in paints, printing ...

, FeTiO₃. We may ask whether the mineral contains Fe²⁺ and Ti⁴⁺, or Fe³⁺ and Ti³⁺. Its crystal structure has each metal atom bonded to six oxygens and each of the equivalent oxygens to two

s and two

titanium Titanium is a chemical element with the symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion i ...

s, as in the bond graph below. Experimental data show that three metal-oxygen bonds in the octahedron are short and three are long (the metals are off-center). The bond orders (valences), obtained from the bond lengths by the bond valence method, sum up to 2.01 at Fe and 3.99 at Ti; which can be rounded off to oxidation states +2 and +4, respectively: : 15oxstate

Balancing redox

Oxidation states can be useful for balancing chemical equations for oxidation-reduction (or

redox Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or ...

) reactions, because the changes in the oxidized atoms have to be balanced by the changes in the reduced atoms. For example, in the reaction of

acetaldehyde Acetaldehyde (IUPAC systematic name ethanal) is an organic chemical compound with the formula CH3 CHO, sometimes abbreviated by chemists as MeCHO (Me = methyl). It is a colorless liquid or gas, boiling near room temperature. It is one of the ...

with Tollens' reagent to form

acetic acid Acetic acid , systematically named ethanoic acid , is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main componen ...

(shown below), the

carbonyl In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups. A compound containi ...

carbon atom changes its oxidation state from +1 to +3 (loses two electrons). This oxidation is balanced by reducing two Ag⁺ cations to Ag⁰ (gaining two electrons in total). : Redox eqn 1

An inorganic example is the Bettendorf reaction using SnCl₂ to prove the presence of arsenite ions in a concentrated

HCl HCL may refer to: Science and medicine * Hairy cell leukemia, an uncommon and slowly progressing B cell leukemia * Harvard Cyclotron Laboratory, from 1961 to 2002, a proton accelerator used for research and development * Hollow-cathode lamp, a s ...

extract. When arsenic(III) is present, a brown coloration appears forming a dark precipitate of

arsenic Arsenic is a chemical element with the symbol As and atomic number 33. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Arsenic is a metalloid. It has various allotropes, b ...

, according to the following simplified reaction: : 2 As³⁺ + 3 Sn²⁺ → 2 As⁰ + 3 Sn⁴⁺ Here three tin atoms are oxidized from oxidation state +2 to +4, yielding six electrons that reduce two arsenic atoms from oxidation state +3 to 0. The simple one-line balancing goes as follows: the two redox couples are written down as they react; :As³⁺ + Sn²⁺ As⁰ + Sn⁴⁺. One tin is oxidized from oxidation state +2 to +4, a two-electron step, hence 2 is written in front of the two arsenic partners. One arsenic is reduced from +3 to 0, a three-electron step, hence 3 goes in front of the two tin partners. An alternative three-line procedure is to write separately the half-reactions for oxidation and reduction, each balanced with electrons, and then to sum them up such that the electrons cross out. In general, these redox balances (the one-line balance or each half-reaction) need to be checked for the ionic and electron charge sums on both sides of the equation being indeed equal. If they are not equal, suitable ions are added to balance the charges and the non-redox elemental balance.

Appearances

Nominal oxidation states

A nominal oxidation state is a general term with two different definitions: *

Electrochemical Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outc ...

oxidation state represents a molecule or ion in the

Latimer diagram A Latimer diagram of a chemical element is a summary of the standard electrode potential data of that element. This type of diagram is named after Wendell Mitchell Latimer, an American chemist. Construction In a Latimer diagram, the most highly ...

Frost diagram A Frost diagram or Frost–Ebsworth diagram is a type of graph used by inorganic chemists in electrochemistry to illustrate the relative stability of a number of different oxidation states of a particular substance. The graph illustrates the free ...

for its redox-active element. An example is the Latimer diagram for

sulfur Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formul ...

at pH 0 where the electrochemical oxidation state +2 for sulfur puts between S and H₂SO₃: :: 16oxstate

* Systematic oxidation state is chosen from close alternatives as a pedagogical description. An example is the oxidation state of phosphorus in H₃PO₃ (structurally

diprotic In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...

HPO(OH)₂) taken nominally as +3, while Allen electronegativities of

phosphorus Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ea ...

and

suggest +5 by a narrow margin that makes the two alternatives almost equivalent: :: 17oxstate

:Both alternative oxidation numbers for phosphorus make chemical sense, depending on which chemical property or reaction is emphasized. By contrast, a calculated alternative, such as the average (+4) does not.

Ambiguous oxidation states

Lewis formula Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons th ...

e are rule-based approximations of chemical reality, as are Allen electronegativities. Still, oxidation states may seem ambiguous when their determination is not straightforward. If only an experiment can determine the oxidation state, the rule-based determination is ambiguous (insufficient). There are also truly dichotomous values that are decided arbitrarily.

Oxidation-state determination from resonance formulas

Seemingly ambiguous oxidation states are derived from a set of

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...

formulas of equal weights for a molecule having heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8 − ''N'' rule. An example is S₂N₂ where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 for the two sulfur atoms, which average to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

A physical measurement is needed to determine oxidation state

* when a non-innocent

is present, of hidden or unexpected redox properties that could otherwise be assigned to the central atom. An example is the

nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...

dithiolate complex, . * when the redox ambiguity of a central atom and ligand yields dichotomous oxidation states of close stability, thermally induced

tautomerism Tautomers () are structural isomers (constitutional isomers) of chemical compounds that readily interconvert. The chemical reaction interconverting the two is called tautomerization. This conversion commonly results from the relocation of a hydr ...

may result, as exemplified by

manganese Manganese is a chemical element with the Symbol (chemistry), symbol Mn and atomic number 25. It is a hard, brittle, silvery metal, often found in minerals in combination with iron. Manganese is a transition metal with a multifaceted array of ...

catecholate, . Assignment of such oxidation states requires spectroscopic, magnetic or structural data. * when the bond order has to be ascertained along with an isolated tandem of a heteronuclear and a homonuclear bond. An example is

thiosulfate Thiosulfate ( IUPAC-recommended spelling; sometimes thiosulphate in British English) is an oxyanion of sulfur with the chemical formula . Thiosulfate also refers to the compounds containing this anion, which are the salts of thiosulfuric acid, e ...

having two possible oxidation states (bond orders are in blue and formal charges in green): :: 21oxstate

:The S–S distance measurement in

is needed to reveal that this bond order is very close to 1, as in the formula on the left.

Ambiguous/arbitrary oxidation states

* when the electronegativity difference between two bonded atoms is very small (as in H₃PO₃). Two almost equivalent pairs of oxidation states, arbitrarily chosen, are obtained for these atoms. * when an electronegative

p-block A block of the periodic table is a set of elements unified by the atomic orbitals their valence electrons or vacancies lie in. The term appears to have been first used by Charles Janet. Each block is named after its characteristic orbital: s-blo ...

atom forms solely homonuclear bonds, the number of which differs from the number of two-electron bonds suggested by

rules Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pert ...

. Examples are homonuclear finite chains like (the central nitrogen connects two atoms with four two-electron bonds while only three two-electron bonds are required by 8 − ''N'' rule) or (the central iodine connects two atoms with two two-electron bonds while only one two-electron bond fulfills the 8 − ''N'' rule). A sensible approach is to distribute the ionic charge over the two outer atoms. Such a placement of charges in a

polysulfide Polysulfides are a class of chemical compounds containing chains of sulfur atoms. There are two main classes of polysulfides: inorganic and organic. Among the inorganic polysulfides, there are ones which contain anions, which have the general formu ...

(where all inner sulfurs form two bonds, fulfilling the 8 − ''N'' rule) follows already from its Lewis structure. * when the isolated tandem of a heteronuclear and a homonuclear bond leads to a bonding compromise in between two Lewis structures of limiting bond orders. An example is N₂O: :: 18oxstate

:The typical oxidation state of nitrogen in N₂O is +1, which also obtains for both nitrogens by a molecular orbital approach. The formal charges on the right comply with electronegativities, which implies an added ionic bonding contribution. Indeed, the estimated N−N and N−O bond orders are 2.76 and 1.9, respectively, approaching the formula of integer bond orders that would include the ionic contribution explicitly as a bond (in green): :: 19oxstate

:Conversely, formal charges against electronegativities in a Lewis structure decrease the bond order of the corresponding bond. An example is

carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...

with a bond-order estimate of 2.6.

Fractional oxidation states

Fractional oxidation states are often used to represent the average oxidation state of several atoms of the same element in a structure. For example, the formula of

is , implying an average oxidation state for iron of +. However, this average value may not be representative if the atoms are not equivalent. In a crystal below , two-thirds of the cations are and one-third are , and the formula may be more clearly represented as FeO·. Likewise,

propane Propane () is a three-carbon alkane with the molecular formula . It is a gas at standard temperature and pressure, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used as ...

, , has been described as having a carbon oxidation state of −. Again, this is an average value since the structure of the molecule is , with the first and third carbon atoms each having an oxidation state of −3 and the central one −2. An example with true fractional oxidation states for equivalent atoms is potassium

superoxide In chemistry, a superoxide is a compound that contains the superoxide ion, which has the chemical formula . The systematic name of the anion is dioxide(1−). The reactive oxygen ion superoxide is particularly important as the product of t ...

, . The diatomic superoxide ion has an overall charge of −1, so each of its two equivalent oxygen atoms is assigned an oxidation state of −. This ion can be described as a

hybrid of two Lewis structures, where each oxygen has an oxidation state of 0 in one structure and −1 in the other. For the cyclopentadienyl anion , the oxidation state of C is −1 + − = −. The −1 occurs because each carbon is bonded to one hydrogen atom (a less electronegative element), and the − because the total ionic charge of −1 is divided among five equivalent carbons. Again this can be described as a resonance hybrid of five equivalent structures, each having four carbons with oxidation state −1 and one with −2. : Finally, fractional oxidation numbers are not used in the description of red lead. is represented as lead(II,IV) oxide, showing the oxidation states of the two nonequivalent

lead Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, ...

atoms.

Elements with multiple oxidation states

Most elements have more than one possible oxidation state. For example, carbon has nine possible integer oxidation states from −4 to +4: :

Oxidation state in metals

Many compounds with luster and

electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...

maintain a simple

stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...

formula, such as the golden TiO, blue-black RuO₂ or coppery ReO₃, all of obvious oxidation state. Ultimately, assigning the free metallic electrons to one of the bonded atoms is not comprehensive and can yield unusual oxidation states. Examples are the LiPb and ordered

alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductili ...

s, the composition and structure of which are largely determined by

atomic size The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there ...

and packing factors. Should oxidation state be needed for redox balancing, it is best set to 0 for all atoms of such an alloy.

List of oxidation states of the elements

This is a list of known oxidation states of the

chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...

s, excluding nonintegral values. The most common states appear in bold. The table is based on that of Greenwood and Earnshaw, with additions noted. Every element exists in oxidation state 0 when it is the pure non-ionized element in any phase, whether monatomic or polyatomic

allotrope Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical State of matter, state, known as allotropes of the elements. Allotropes are different structural modifications o ...

. The column for oxidation state 0 only shows elements known to exist in oxidation state 0 in compounds.

Early forms (octet rule)

A figure with a similar format was used by

Irving Langmuir Irving Langmuir (; January 31, 1881 – August 16, 1957) was an American chemist, physicist, and engineer. He was awarded the Nobel Prize in Chemistry in 1932 for his work in surface chemistry. Langmuir's most famous publication is the 1919 ar ...

in 1919 in one of the early papers about the

octet rule The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rul ...

. The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule. : Langmuir valence

Use in nomenclature

The oxidation state in compound naming for

transition metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...

s and lanthanides and

actinides The actinide () or actinoid () series encompasses the 15 metallic chemical elements with atomic numbers from 89 to 103, actinium through lawrencium. The actinide series derives its name from the first element in the series, actinium. The inform ...

is placed either as a right superscript to the element symbol in a chemical formula, such as Fe^III or in parentheses after the name of the element in chemical names, such as iron(III). For example, is named iron(III) sulfate and its formula can be shown as Fe. This is because a

sulfate ion The sulfate or sulphate ion is a polyatomic anion with the empirical formula . Salts, acid derivatives, and peroxides of sulfate are widely used in industry. Sulfates occur widely in everyday life. Sulfates are salts of sulfuric acid and many ar ...

has a charge of −2, so each iron atom takes a charge of +3.

History of the oxidation state concept

Early days

Oxidation itself was first studied by

Antoine Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

(hence the name). The term has since been generalized to imply a ''formal'' loss of electrons. Oxidation states, called ''oxidation grades'' by

Friedrich Wöhler Friedrich Wöhler () FRS(For) Hon FRSE (31 July 180023 September 1882) was a German chemist known for his work in inorganic chemistry, being the first to isolate the chemical elements beryllium and yttrium in pure metallic form. He was the fi ...

in 1835, were one of the intellectual stepping stones that

Dmitri Mendeleev Dmitri Ivanovich Mendeleev (sometimes transliterated as Mendeleyev or Mendeleef) ( ; russian: links=no, Дмитрий Иванович Менделеев, tr. , ; 8 February Old_Style_and_New_Style_dates">O.S._27_January.html" ;"title="O ...

used to derive the

periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...

. William B. Jensen gives an overview of the history up to 1938.

Use in nomenclature

When it was realized that some metals form two different binary compounds with the same nonmetal, the two compounds were often distinguished by using the ending ''-ic'' for the higher metal oxidation state and the ending ''-ous'' for the lower. For example, FeCl₃ is

ferric chloride Iron(III) chloride is the inorganic compound with the formula . Also called ferric chloride, it is a common compound of iron in the +3 oxidation state. The anhydrous compound is a crystalline solid with a melting point of 307.6 °C. The col ...

and FeCl₂ is ferrous chloride. This system is not very satisfactory (although sometimes still used) because different metals have different oxidation states which have to be learned: ferric and ferrous are +3 and +2 respectively, but cupric and cuprous are +2 and +1, and stannic and stannous are +4 and +2. Also, there was no allowance for metals with more than two oxidation states, such as

vanadium Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery-grey, malleable transition metal. The elemental metal is rarely found in nature, but once isolated artificially, the formation of an oxide layer ( pass ...

with oxidation states +2, +3, +4, and +5. This system has been largely replaced by one suggested by Alfred Stock in 1919 and adopted by

in 1940. Thus, FeCl₂ was written as

iron(II) chloride Iron(II) chloride, also known as ferrous chloride, is the chemical compound of formula FeCl2. It is a paramagnetic solid with a high melting point. The compound is white, but typical samples are often off-white. FeCl2 crystallizes from water a ...

rather than ferrous chloride. The Roman numeral II at the central atom came to be called the " Stock number" (now an obsolete term), and its value was obtained as a charge at the central atom after removing its ligands along with the

electron pair In chemistry, an electron pair or Lewis pair consists of two electrons that occupy the same molecular orbital but have opposite spins. Gilbert N. Lewis introduced the concepts of both the electron pair and the covalent bond in a landmark paper he ...

s they shared with it.

Development towards the current concept

The term "oxidation state" in English chemical literature was popularized by

Wendell Mitchell Latimer Wendell Mitchell Latimer (April 22, 1893 – July 6, 1955) was an American chemist notable for his description of oxidation states in his book "The Oxidation States of the Elements and Their Potentials in Aqueous Solution" (ASIN B000GRXLSA, ...

in his 1938 book about electrochemical potentials. He used it for the value (synonymous with the German term ''Wertigkeit'') previously termed "valence", "polar valence" or "polar number" in English, or "oxidation stage" or indeed the "state of oxidation". Since 1938, the term "oxidation state" has been connected with electrochemical potentials and electrons exchanged in redox couples participating in redox reactions. By 1948, IUPAC used the 1940 nomenclature rules with the term "oxidation state", instead of the original ''valency''. In 1948

Linus Pauling Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topi ...

proposed that oxidation number could be determined by extrapolating bonds to being completely ionic in the direction of

. A full acceptance of this suggestion was complicated by the fact that the Pauling electronegativities as such depend on the oxidation state and that they may lead to unusual values of oxidation states for some transition metals. In 1990 IUPAC resorted to a postulatory (rule-based) method to determine the oxidation state. This was complemented by the synonymous term oxidation number as a descendant of the Stock number introduced in 1940 into the nomenclature. However, the terminology using "

ligands In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...

" gave the impression that oxidation number might be something specific to

coordination complex A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as '' ligands'' or complexing agents. M ...

es. This situation and the lack of a real single definition generated numerous debates about the meaning of oxidation state, suggestions about methods to obtain it and definitions of it. To resolve the issue, an IUPAC project (2008-040-1-200) was started in 2008 on the "Comprehensive Definition of Oxidation State", and was concluded by two reports and by the revised entries "Oxidation State" and "Oxidation Number" in the IUPAC Gold Book. The outcomes were a single definition of oxidation state and two algorithms to calculate it in molecular and extended-solid compounds, guided by Allen electronegativities that are independent of oxidation state.

References

{{Oxide Chemical nomenclature Chemical properties Coordination chemistry Dimensionless numbers of chemistry Redox

IUPAC definition

Determination

Simple approach without bonding considerations

Algorithm of assigning bonds

The algorithm's caveat

Algorithm of summing bond orders

Applied to a Lewis structure

Applied to bond graph

Balancing redox

Appearances

Nominal oxidation states

Ambiguous oxidation states

Oxidation-state determination from resonance formulas

A physical measurement is needed to determine oxidation state

Ambiguous/arbitrary oxidation states

Fractional oxidation states

Elements with multiple oxidation states

Oxidation state in metals

List of oxidation states of the elements

Early forms (octet rule)

Use in nomenclature

History of the oxidation state concept

Early days

Use in nomenclature

Development towards the current concept

See also

References